A new signature-based algorithms for computing Gröbner bases
A new signature-based algorithms for computing Gröbner bases
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DOI：
10.1007/s11424-015-2260-z
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发表时间：
2015-01
影响因子：
2.1
通讯作者：
Licui Zheng;Jinwang Liu;Weijun Liu;Dongmei Li
中科院分区：
文献类型：
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作者：
Licui Zheng;Jinwang Liu;Weijun Liu;Dongmei Li
Gao，Volny and Wang（2010）给出了一个基于签名的算法计算Gröbner基的简单标准。它给出了计算理想和合偶的Gröbner基的统一框架，合偶基在同调代数的自由分解中是非常重要的。Sun和Wang（2011）后来将GVW标准推广到更一般的情况（包括F5算法）。基于签名的算法在计算Gröbner基方面越来越受欢迎。本文引入了因子对的概念，可以用来检测比广义GVW准则更多的无用J-对，从而改进基于签名的算法。
Gao, Volny and Wang (2010) gave a simple criterion for signature-based algorithms to compute Gröbner bases. It gives a unified frame work for computing Gröbner bases for both ideals and syzygies, the latter is very important in free resolutions in homological algebra. Sun and Wang (2011) later generalized the GVW criterion to a more general situation (to include the F5 Algorithm). Signature-based algorithms have become increasingly popular for computing Gröbner bases. The current paper introduces a concept of factor pairs that can be used to detect more useless J-pairs than the generalized GVW criterion, thus improving signature-based algorithms.